Patients with acute or serious infections, such as Salmonella typhi or gram-negative bacteria causing meningitis, can be successfully treated with regular doses of Chloramphenicol. A patient weighing 150 pounds requires a dose of 850 milligrams, while a patient weighing 300 lbs requires a dose of 1700 milligrams.

Question

Lab experiments have indicated that the concentration level C, in micrograms per milliliter (mcg/ml), of the medication in the a patient’s bloodstream as a function of the amount of time t, in hours, since the medication is administered is given by the quadratic function:
C(t)= -1.152t^2 + 8.064t + 4.288. For a drug to have a beneficial effect, its concentration in the bloodstream must exceed a certain value, called the minimum therapeutic level. The minimum therapeutic level of Chloramphenicol is 8 mcg/ml.

Determine a linear function for determining the dosage needed for a patient based on the patient’s weight, in pounds.